The Ukrainian authorities have trumpeted a turning point in the three-month conflict with separatists in the east after retaking a town at the epicentre of the breakaway movement.

The breakthrough came after the president, Petro Poroshenko, ignored calls from both Russia and the EU to extend a ceasefire that ran out a week ago and decided to go on the attack. Ukrainian forces seized the town of Slavyansk on Saturday, ending a protracted standoff that left dozens dead and reduced parts of the town to rubble.

"It's not a total victory. But the purging of Slavyansk of these bands, made up of people armed to the teeth, has incredible symbolic importance," said Poroshenko in a statement.

On Sunday, Ukrainian authorities said they had taken full control over a number of other towns that had been seized by separatists, including Kramatorsk, Artemovsk and Druzhovka.

But it is the capture of Slavyansk, abandoned by the fighters after some initial clashes, that is the most significant psychological boost for Kiev.

The town of around 100,000 people had become the epicentre of the fighting, surrounded by armed checkpoints. It has undergone food and water shortages in recent weeks as Ukrainian forces have encircled it, and there have been civilian casualties from Ukrainian shelling. Almost half the population have fled, many to refugee camps in Russia, and Kiev now faces a sizeable task to win back the population.

The separatist fighters abandoned Slavyansk in a hurry, setting fire to documents in the security services building that they had made their headquarters for the past three months and mining one of the rooms before leaving, which was cordoned off and exploded by arriving Ukrainian forces. A number of hostages – mainly pro-Ukrainian journalists and activists – were freed.

On 2 July the foreign ministers of Russia, Ukraine, France and Germany met in Berlin and agreed on further negotiations, and over the weekend Russia's foreign ministry again called on both sides to lay down arms and demanded talks between Kiev and the separatists. However, Poroshenko has clearly decided the time has come to go on the attack.

"My order is now in effect – tighten the ring around the terrorists," the president posted on Twitter after Slavyansk was regained. "Continue the operation to liberate Donetsk and Luhansk regions."

There were signs that rebels from Slavyansk were falling back on the regional capital, Donetsk, to continue the resistance. Igor Girkin, the military commander of Slavyansk, told the Russian agency Life News that he had arrived in Donetsk.

"We will continue the combat operations and will try not to make the same mistakes that we made in the past," said Girkin, a Russian also known by his nom de guerre, Igor Strelkov. Thousands turned out to rally behind the rebels in Donetsk on Sunday afternoon.

Girkin has been one of the most intriguing characters of the uprising. A Russian citizen with apparent links to military intelligence, he was previously known for enjoying costumed military re-enactments, and has been an elusive figure since he emerged as the figurehead of the Slavyansk resistance, giving interviews to only a few trusted Russian correspondents and issuing decrees threatening to shoot people for desertion or looting.

The separatist leader Pavel Gubarev read out a message from Girkin to the crowds in Donetsk, in which the commander compared the flight from Slavyansk to the decision by the Russian army to abandon Moscow in 1812. Without that, Girkin said, Russia would not have defeated Napoleon and marched on Paris, and for the same reason the fighters had left Slavyansk to regroup and eventually drive Kiev's armies from the east before marching on the capital itself.

However, with Slavyansk back under Kiev's control, numerous casualties among the separatists and no sign that Russia has any appetite to become more officially involved in the conflict, it appears that the tide may have turned.

Poroshenko faces a decision on whether to attempt a final and decisive victory over the separatist movement by taking on the fighters in Donetsk and Luhansk, major urban conurbations where civilian casualties would appear to be likely.

Already, there is a huge amount of anger in the east over some of the methods used during the "anti-terrorist operation" to rid the east of fighters, much of which has relied on hastily assembled volunteer battalions.

Tanya Lokshina, of Human Rights Watch, called on the Ukrainian authorities to mount a "thorough and impartial investigation" into apparent air strikes on villages near Luhansk that killed a number of civilians including a five-year-old boy, according to witnesses.